33. Your friend wants to make a bet with you: You bet $30 and roll a fair, 6-sided die.If you roll a 1,you win $120. But ifyou roll any other number, you lose$30.

a) What is the expected monetary value of taking the bet?

b) Conceptually speaking, what does this mean?

c) What is the fair price of thebet?

34. You are deciding whether to buy one of two vehicles: a Jeep Wrangler or a Toyota Prius. The price for the Jeep is $25,000while the Prius is $30,000.You also take into account their fuel-efficiency. The Jeep gets about 16 miles per gallon (mpg) and the Prius gets about 50 mpg. Say that over the life of the vehicle, you will drive 100,000 miles. Under this condition, the Jeep would use approximately 6,250 gallons total, while the Prius would use 2,000 gallons. But, you are uncertain about what gas prices will be in the future. In your mind, you could pay an average price of $2 per gallon over the life of the vehicleoran average price of $4 per gallon.

The following decision table represents the costs associated with buying either vehicle under eachpossible state of affairs:

	Gas = $2/gal.	Gas = $4/gal.
Jeep	-$37,500	-$50,000
Prius	-$34,000	-$38,000

a) According to the Dominance Rule, which vehicleshould you buy?Why?

b)After doing some research, you estimate that it is much more likely that gas prices will increase in the future. You estimate that the Pr($2/gal.) = 20%and that the Pr($4/gal.) = 80%. Taking these two probabilities into consideration, find the expected value of buying the Jeep (J) and buying the Prius (P).

Exp(J) =

Exp(P) =